Loop Representation of the Partition Function of Lattice U(1) Gauge Theory

We introduce in a natural and straigthforward way the $loop$ (Lagrangian) $representation$ for the partition function of pure compact lattice QED. The corresponding classical lattice loop action is proportional to the quadratic area of the loop world sheets. We discuss the parallelism between the $loop$ formulation of this model in terms of world sheets of loops and the $topological$ representation of the Higgs (broken) phase for the non-compact lattice QED in terms of world sheets of Nielsen-Olesen strings.